# Amarts and Set Function Processes by A. Gut, K. D. Schmidt

By A. Gut, K. D. Schmidt

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1982), A contribution to the theory of asymptotic martingales. Glasgow Math. J. 23, 177-186. , (1974), On stopping rules and the expected supremum of Sn/a n and ISnl/a n . Ann. Probability 2, 899-905. Krengel, U. , (1978), On semiamarts, amarts and processes with finite value. Advances in Prob. 4, 197-266. , Van Nostrand, Princeton. , (1972), Th~orie des processus stochastiques g~n~raux; applications aux surmartingales. Z. Wahrscheinlichkeltstheorie verw. Gebiete 22, 45-68. , (1966), Probabilit~s et Potentiel.

The M e a s u r e s . principal generalized measure This purpose with respect construction measures, measures norm. which to a on an a l g e b r a operator the A L - s p a c e F with additive) on the L e b e s g u e of all each bounded measure extension ~(A+B) = > ~ ~(A) for e a c h p a i r fact the b o u n d e d to the v a r i a t i o n in p r o v i n g its g e n e r a l i z e d of the c l a s s i c a l vector measure. for b o u n d e d that respect additive) that the Radon-Nikodym Radon-Nikodym lattice homomorphism on measures.

Theoretical and it is a l s o m o t i v a t e d generalized rather of set f u n c t i o n in terms of the e x p e c t a t i o n s from b o u n d e d each derivatives, and their expectations. in the p r o p e r t i e s of set f u n c t i o n of amarts c a n be d e v e l o p e d Furthermore, Radon-Nikodym measure theoretical In the f r a m e w o r k of b o u n d e d a d d i t i v e to a m a r t t h e o r y of amarts theoretic are i n d e x e d by the p o s i t i v e random variables we will be i n t e r e s t e d processes, a measure study a m a r t s and their g e n e r a l i z e d of i n t e g r a b l e More generally, amarts.